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Geometrical expression of excess entropy production
Takahiro Sagawa1, Hisao Hayakawa
1The Hakubi Center, The Kyoto University, Yoshida-Ushinomiya-cho, Sakyo-ku, Kyoto, Japan.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 21, 2011
Summary
We developed a geometric formula for excess entropy production in nonequilibrium systems. This new approach simplifies calculations for complex, nonlinear processes and reveals connections to quantum mechanics.
Area of Science:
- * Statistical Mechanics
- * Non-equilibrium Thermodynamics
- * Stochastic Processes
Background:
- * Understanding entropy production is crucial for characterizing the irreversibility of thermodynamic processes.
- * Current methods often struggle with nonlinear and non-equilibrium systems.
- * Markovian jump processes are fundamental models for systems with discrete states and transitions.
Purpose of the Study:
- * To derive a general geometrical expression for excess entropy production.
- * To apply this expression to quasistatic transitions between non-equilibrium steady states.
- * To explore the implications for the thermodynamics of non-equilibrium systems.
Main Methods:
- * Derivation of a geometrical formula for excess entropy production.
- * Analysis of quasistatic transitions in Markovian jump processes.
- * Comparison of the geometrical expression to the Berry phase in quantum mechanics.
Main Results:
- * A novel geometrical expression for excess entropy production was derived.
- * This expression is applicable to nonlinear and non-equilibrium situations.
- * Excess entropy production was shown to depend on parameter space trajectories, similar to the Berry phase.
Conclusions:
- * The derived geometrical expression offers a new perspective on entropy production.
- * The findings suggest a deep connection between non-equilibrium thermodynamics and geometry.
- * Vector potentials are implied to be essential for a complete thermodynamics of non-equilibrium steady states.
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